Defining parameters
| Level: | \( N \) | \(=\) | \( 4212 = 2^{2} \cdot 3^{4} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4212.p (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 39 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1512\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4212, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1584 | 112 | 1472 |
| Cusp forms | 1440 | 112 | 1328 |
| Eisenstein series | 144 | 0 | 144 |
Decomposition of \(S_{2}^{\mathrm{new}}(4212, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4212, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4212, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(702, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1053, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1404, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2106, [\chi])\)\(^{\oplus 2}\)